The Dried Product - Freeze-drying of Pharmaceuticals and Biopharmaceuticals - page 159

Table 1 Water layers surrounding spherical sucrose particles at 0.1% residual
water content

Surface area (cm 2 g 1 ) Water molecular layers (mm) Water layers

1 38,000 1.1

10 3800 11

38 1000 42

100 380 110

described in the following paragraphs in increasing order of the neces-
sary experimental effort.
From a knowledge of the crystal-melting temperature, T m , the glass
temperature can be estimated with some degree of confidence, at least for
many of the excipients commonly used for freeze-dried pharmaceutical
preparations, where it has been found empirically that T g /T m

0.73.
Furthermore, for the same preparations, the temperature of zero mobility
can be approximated by T o

E

E
100 kJ g 1 .AtT g , the viscosity of most glasses is assumed to lie between
10 11 and 10 13 Pa s, and above T g , the viscosity often follows the WLF
equation. It is thus possible to obtain T o at (T 4 T g ). As shown
previously, the fragility can be obtained from carefully performed DSC
heating scans, with the aid of measured values for DC g , T g /T m and DT g .
From the ideal mixing rules and the Gordon-Taylor equation, 95 an
estimate can be obtained for the effect of sorbed water on T g . It is thus
possible to determine the critical plasticiser content at which T g corre-
sponds to the ambient temperature. A fully amorphous sample can then
be prepared by quenching a fused preparation into a cryogen, followed
by freeze-drying or spray drying to complete dryness. The thermophys-
ical characteristics of the fully amorphous, anhydrous substance can
then be obtained. Water vapour sorption measurements should then be
performed at several temperatures. The recrystallisation characteristics
above T g in the anhydrous state and in the presence of water vapour at a
range of relative humidities can now be determined. Powder X-ray
diffraction studies will indicate whether the substance crystallises as a
hydrate and/or a metastable polymorph, such as might introduce me-
chanical/chemical instability. In order to estimate stability below T g ,itis
necessary to determine enthalpic (also structural and/or chemical) re-
laxation rates under different conditions.
A direct experimental method that does not rely on approximations
and assumptions has been reported by Ahmed et al. 147 It is based on a
combination of DSC with isothermal calorimetry and powder X-ray
diffraction. It is particularly useful for the detection of low amounts of
amorphous material in allegedly crystalline drug products.

E

T m /2. Also, for many materials, DC g T g